Last 3 questions thank you so much

Step-by-step explanation:

1)  

we are given ∠17  and the Adj = 200 meters they want to know the Opp

so use  TOA

Tan(17) = Opp / 200

200*Tan(17) = Opp

61.146 = Opp

the mast stands 61.1 meters tall   ( rounded to nearest 10th )

2)

now we know the opp = 40 meters and the angle is 35° and Adj = x

Use TOA again, but w/ the different knowns

Tan(35) = 40 / Adj

Adj = 40 / Tan(35)

57.1259 = Adj

so the boat is 57.1 meters from the cliff  ( rounded to nearest 10th)

3)

we are given two triangles now and are told to find the difference between them to find the distance between the buoys

Opp = 70

∠A = 60

∠B = 40

we want to find the Adj for each so use TOA

for A , then

Tan(60)= 70/a

a = 70 / Tan(60)

a = 40.4145

for B, then

Tan(40) = 70 /b

b = 70 / Tan(40)

b = 83.4227

so subtract  a  from b

83.4227 - 40.4145 = 43.008

so from buoy A to buoy B is 43.0 meters ( rounded to nearest 10th )

:)

it has 4

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